Holt CA Course 1 4-6 Solving Equations Containing Fractions AF1.1 Write and solve one-step linear equations in one variable. Also covered: NS2.1, NS2.2,

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Holt CA Course Solving Equations Containing Fractions AF1.1 Write and solve one-step linear equations in one variable. Also covered: NS2.1, NS2.2, NS2.4 California Standards

Holt CA Course Solving Equations Containing Fractions The goal when solving equations that contain fractions is the same as when working with other kinds of numbers—to get the variable by itself on one side of the equation.

Holt CA Course Solving Equations Containing Fractions Solve. Write the answer in simplest form. Example 1A: Solving Equations by Adding or Subtracting x – 3737 = = = x= 8787 = Simplify Since is subtracted from x, 3737 add to both sides.

Holt CA Course Solving Equations Containing Fractions Solve. Write the answer in simplest form. Example 1B: Solving Equations by Adding or Subtracting t = t = 5 12 Find a common denominator. Subtract t –= 5 12 – t = – 9 24 t = 1 24 Since is added to t, subtract from both sides.

Holt CA Course Solving Equations Containing Fractions Solve. Write the answer in simplest form. Additional Example 1C: Solving Equations by Adding or Subtracting r = r = r – 4949 = 1212 – 4949 Find a common denominator. Subtract. r = 1 18 – r = Since is added to r, subtract from both sides.

Holt CA Course Solving Equations Containing Fractions Check. Additional Example 1C Continued r = 1212 = Find a common denominator. Add. You can check that a value is a solution to an equation by substituting the value for the variable. Helpful Hint Substitute for r = ? = ?

Holt CA Course Solving Equations Containing Fractions Solve. Write the answer in simplest form. Check It Out! Example 1B y = y = y – = – y = – 2828 y = 1818 Find a common denominator. Subtract. Since is added to y, subtract from both sides

Holt CA Course Solving Equations Containing Fractions Check. Check It Out! Example 1B Continued y = 3838 = Find a common denominator. Add. Substitute for y = ? = ?

Holt CA Course Solving Equations Containing Fractions Solve. Write the answer in simplest form. Check It Out! Example 1C t = t = 2727 Find a common denominator. Subtract t – = 2727 – t = – t = 1 14 Since is added to t, 3 14 subtract from both sides. 3 14

Holt CA Course Solving Equations Containing Fractions Solve. Write the answer in simplest form. Example 2A: Solving Equations by Multiplying 3838 x = x =   =x 2323 Multiply by the reciprocal of Then simplify = 1414 x = To undo multiplying by Caution! 3838, you can divide by 3838 or multiplyby its reciprocal, 8383.

Holt CA Course Solving Equations Containing Fractions Additional Example 2B: Solving Equations by Multiplying 4y = y4y =   y = y = Multiply by the reciprocal of 4. Then simplify. Solve. Write the answer in simplest form.

Holt CA Course Solving Equations Containing Fractions Solve. Write the answer in simplest form. Check It Out! Example 2A 3434 x = x= =x 2323 Multiply by the reciprocal of Then simplify = 1212 x =

Holt CA Course Solving Equations Containing Fractions Example 3: Physical Science Application The amount of copper in brass is of the total weight. If a sample contains 4 ounces of copper, what is the total weight of the sample? Let w represent the total weight of the sample w = w  4343 =  4343 w = 21 5  w = 28 5 or Write an equation. Multiply by the reciprocal of 3434 · Write as an improper fraction. Then simplify. The sample weighs ounces.

Holt CA Course Solving Equations Containing Fractions Solve. Write the answer in simplest form. Check It Out! Example 1 x – 3838 = = = x = 10 8 = Simplify. Since is subtracted from x, add to both sides

Holt CA Course Solving Equations Containing Fractions Check It Out! Example 2 3y = y=   y = y = 3 Multiply by the reciprocal of 3. Then simplify. Solve. Write the answer in simplest form.

Holt CA Course Solving Equations Containing Fractions The amount of copper in zinc is of the total weight. If a sample contains 5 ounces of copper, what is the total weight of the sample? Check It Out! Example Let w represent the total weight of the sample w = w  4141 =  4141 w = 16 3  4141 w = 64 3 or Write an equation. Multiply by the reciprocal of 1414 · Write as an improper fraction. Multiply. The sample weighs ounces.